Primordial element (algebra)
In algebra, a primordial element is a particular kind of a vector in a vector space. Let V be a vector space over a field k and fix a basis for V of vectors for . By the definition of a basis, every vector v in V can be expressed uniquely as
Define , the set of indices for which the expression of v has a nonzero coefficient. Given a subspace W of V, a nonzero vector w in W is said to be "primordial" if it has the following two properties:[1]
- is minimal among the sets , and
- for some i
References
- ↑ Milne, J., Class field theory course notes, updated March 23, 2013, Ch IV, §2.
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